The Design, Control And Synchronization Of Chaotic System

Chaotic signal is a kind of signal which is seemingly random, extremely sensitive to initial conditions generated by nonlinear system. And it is concerned in the field of secure communication, signal processing, image processing and so on. The design and analysis of chaotic system have a vital role in the applications of chaos. Through theoretical analyses and numerical simulations, we studied the establishment, control of chaos and mixed synchronization. The main researches are as follows.The establishment of chaos:based on the features of some existing chaotic systems, a novel four-dimensional dynamical system with a new architecture is constructed by recombining the state variables of the Qi three-dimensional chaotic system. At the same time, in order to build the circuit easily, some limiting parameters were set to reduce the impact of product terms. Relative to the Qi system, it makes the new system more complex by introducing the disturbance of x4, improving system dimensions. The basic dynamic characteristics of the new chaotic system were analyzed. And the integer-order and fractional-order circuits have been achieved respectively. The results of numerical simulations and circuit experiment showed the existence of a new butterfly attractor.Chaotic control:according to the characteristics of the new system, two time-switched and two phase-switched functions were introduced into it. Then different types of multi-scroll chaotic system were generated by controlling different system variables. On the other hand, a hyper-chaotic model has been established by introducing a negative feedback. The discovery of the new system enriches the family of chaotic systems, and provides a practical model for chaotic applications like secure communication.Chaotic synchronization:the modified hyper chaotic system was used to be a chaotic synchronization model. The synchronization between two systems with same structure is achieved based on the Lyapunov stability theory, and the determination of some relevant synchronous feedback coefficients was discussed. Furthermore, the synchronization control between hyper chaotic Lorenz system and the modified hyper chaotic system is investigated. The good chaotic synchronization shows that the application in secure communication is effective through chaotic masking. Finally, two hyper chaotic systems with uncertain parameters and different structures are synchronized in a generalized way. The simulation results show that the design method of synchronization controller can realize a rapid synchronization between two systems.